uh, I dunno

I cant wait until this book is finally out.

Don't know, maybe some cultural thing. As long as he is not kissing anyones feets...

Is this problem guaranteed to have a solution?

Wow, that's a homework question for children somewhere?

Yes, and it is involved.

Yeah, there is this strange feeling of emptiness when an answer of mine gets accepted with zero upvotes.

I agree. If blindman is a kid, his need for exercise books on functional analysis is quite impressive...

I guess one could puzzle someone by downvoting and accepting an answer at the same time.

I checked it too. The question was clearly improved a lot by the edits, but that is certainly acceptable. and it's only the third questio of tha user.

Downvotin because a solution doesn't minimze length is ridiculous.

I mostly agree, but I sometimes use it for hidden rants like this: math.stackexchange.com/questions/157127/negative-versus-minus

Where would one actually look that up?

http://english.stackexchange.com/questions/45663/how-to-speak-mathematics

Somewhere on MSE I think it was JDH talking about recording lectures and blind students being able to speed them up to ten times faster in order to understand them at the pace similar to how nonblind persons can read formulae

ah, http://math.stackexchange.com/questions/35496/is-there-a-definitive-guide-to-speaking-mathematics/36862#36862

i hope this is right, i'm always screwing up these kinds of arguments: math.stackexchange.com/a/227328/1284

first version was totally wrong and now i think i fixed it

the question is to prove that any such function has an infinite set of discontinuities no?

otherwise you could create one bijection [0,1/2)->[0,1] and another bijection [1/2,1]->[0,1] and glue them together

i thought the problem with 2abs(x)-1 is that 1/2 occurs only once?

oh i see what you mean though

that is an easier way to look at it

i'm always trying to use these "well order R" arguments inappropriately

@anon same stanley as enumerative? hmm.

yup

@JasperLoy That's simple, perpendicular bisector.

at least maybe it's not wrong.

@anon Isn't this question exactly the reason why so many different people have different styles of exposition?

I do not understand what the OP means by this "but I encounter many problems trying to express mathematical formulas since they are written and I do not know how to read them. "

The op means express vocally.

also i have a question i am trying to formulate maybe someone can help...

dirichlet's theorem on arithmetic progressions says that the asymptotic density of primes of the form a*n+b with (a,b) = 1 is 1/phi(a) ...

right

rather 1/phi(a) * (1/log(n)) i believe is right....

that's not a number (it's a function of n), so how can it be an asymptotic density?

anyway what i'm wondering and trying to articulate is, is there some n as a function of a at which this density tends to peak before going about the process of converging to its limit?

rather we can say the asymptotic density of the ratio of the number of primes of the form a*n+b < x with (a,b)=1 to the number of primes < x is 1/phi(a)

that's a mouthful but right i hope

but my question is about the short-term behavior

right, I guess we should say it's a relative asymptotic density (relative to the set of primes)

ok

the ratio will oscillate a lot in the limit and it's unclear what the conditions are to make a value a peak, such that there is a uniquely defined peak value for every a

like e.g., what if it was the case that that pi_a(n) is particularly larger than expected on the basis of dirichlet's theorem for n some fast-growing function of a, like n = 2^a for example

is there any simple function that has that property

it doesn't have to be a unique peak

you would have to quantify "larger-than-expected" in terms of higher-order terms because the limiting ratio will be the same for any subsequence of naturals

but maybe the "first" peak in some sense

well what is expected is exactly pi(n)/phi(a)

or we could say n/(log(n) phi(a)) instead

or Li even. also does the behavior depend on what version of the problem?

so any n for which actual-count-value is greater than n/log(n) phi(a)? seems sort of lame.

"version of the problem" what problem?

yeah i guess an interesting amount of excess has to be quantified

problem right now is just defining the problem :)

holy pancakes nothing on ncatlab makes any sense to me

i remember what motivated the idea if that helps

surely they could make things a little more readable to non category theorists ...

i was wondering if it's faster to find the next prime after n by checking n+1, n+2, etc. until it is found, or instead to skip by some function of n such as n+floor(log(n)), n+floor(log(n+floor(log(n)))), etc....

so that led to the idea that it might work if there is a "sweet spot" for certain arithmetic progressions

i don't mean find the next prime after n, but to find any prime after n by either of the two methods

i guess i can do some experiments and look for any evidence of what i mean

smells like it might be intro level analytic number theory though

i sort of understand how zeros of zeta cause periodicities in the error term of the prime counting function and that seems related

anyway i guess i'm hoping for some theoretical insight before i bother writing programs

basically i had been continuing my line of thought from my monologue on gerry's answer here math.stackexchange.com/a/226465/1284 . one version of the problem is how to find any prime following n in time O(log(n)^k) ?

maybe i'll just ask that.

hi @JasperLoy

Interesting - if groups $G,H$ are considered as one-object categories, two homomorphisms $G\to H$ are naturally isomorphic as functors iff they lie in the same $\mathrm{Inn}(H)$-orbit. I wonder if that's relevant to the discussion here about why conjugation is more naturally a "perspective change" with respect to group actions than generic automorphisms.

1am

@JasperLoy: The lord of the flight.

@JasperLoy: youtube.com/watch?feature=player_embedded

@JasperLoy: The lord of the flight.

@ガベージコレクタ hi

@JasperLoy or her

@JasperLoy: Hi honey , youtube.com/watch?v=cBlRbrB_Gnc

@JasperLoy "Garbage collection" is the literal translation.

@skullpatrol hi...

@JasperLoy oh my ghost :-)

@JasperLoy But you are sweet :-D

good morning

hi

@JohanLarsson Good afternoon. :-)

@skullpatrol Garbage Collector is the correct translation.

@JohanLarsson Did you try LaTex.SE with your question?

the auto render question?

@skullpatrol We usually abbreviate it as TeX.SeX rather than LaTex.SE. :-)

Triying $\LaTeX{}$

makes sence

@JohanLarsson yep

@skullpatrol No did not try it yet, been sleeping

Also you were comparing two things....

I was comparing? (Still tired here but in a different way)

@JasperLoy banana?

Speaking of low hanging fruit

I found that lol^^

ok asked math.stackexchange.com/questions/227363/…

@DanBrumleve +1

and another quickie math.stackexchange.com/questions/227365/…

wow 3 minutes to write that i am impressed with myself

and y'all for helping me learn to do it of course

" You cannot teach a man anything; you can only help him discover it in himself."

sure give me all the credit

i might start thinking too highly of myself

Guess who said that?

i was gonna say einstein but it's way older eh

Galileo

Who said lead the horse to water?

moses?

and my problem is apparently open! hooray!

i'm satisfied by the confirmation of my intuition that it was hard.

I dunno, did not find on google either

Good help is hard to find these days :-D

i used to hate corporate speak but somehow i warmed up to it

nowadays i'm more proactive

it is a convenient shorthand that helps everyone be more lazy.

gotta go to work

later

why is this guy commenting on my q confused? math.stackexchange.com/questions/227365/…

am i using weird notation?

(is my question nonsense?)

@DanBrumleve Invite him into chat.

++skeletor done

nobody pays attention to that "continue in chat" message

this dude does chat.stackexchange.com/rooms/6308/…

He must be a "nobody"?

or probably relatively new to the site :-D

by "smallest" i meant to exclude c+1 c+\omega etc.

oops wrong room

LOL

he is new.

and the discussion is productive.

I'm glad to see the "black hole" of productivity can generate a small productive "white hole."

That^ ties things up nicely ;-)

ha ha

haven't seen any mods here in a while i guess it's been peaceful

There was one here yesterday.

He deleted some sexist remarks...

yeah where is the delete link anyway?

I don't know.

btw is there a standard notation for the smallest ordinal equipollent to R?

$\Omega$ refers to the first uncountable ordinal which is only R if CH is true

$\beth_1$ or $c$ is the cardinality of R.

but what is the notation for its minimal ordinal?

in my head i just call it $c$ but i'm not sure of any unambiguous way to communicate it

@DanBrumleve You're in the wrong room again :)

hi @Sathya

@DanBrumleve Pardon me.

i flagged my own post since i couldn't find delete.

and i got an answer from the newb. i don't understand it yet though.

"Delete" expires after 2 minutes.

ic

check yourself before u wreck yourself

wise

busted math.stackexchange.com/questions/227365/…

@Sathya are you ignoring me?

i thought he was the mod who just showed up to delete my flagged comment.

@JasperLoy: Hey, where are you?

@DanBrumleve Me too.

@ガベージコレクタ I'm thinking of changing my name to "skeletor" what do you think?

skeletor is a mod?

@DanBrumleve Not that I know of.

@skullpatrol: I think you need to change your display name to Moderator or Administrator or something like that. :-)

@skullpatrol: Moderator is the best choice I think!

@ガベージコレクタ Why?

@skullpatrol To be more interesting :-)

@ガベージコレクタ So I'm not interesting enough?

@skullpatrol: Your current display name is not so interesting.

@skullpatrol: Or you can change your name to Jasper Loy, so I will be confused then. :-)

@ガベージコレクタ Why, do you like to be confused?

@skullpatrol: Yes. Because it is fun!

@skullpatrol: it is fun and funny!

@ガベージコレクタ Do you find confusing yourself fun?

@skullpatrol: Yes. Of course.

a visual proof

I don't understand how a skeleton can be muscular?

got too interested in writing random stuff instead.

50 year old human being youtube.com/watch?v=HiVLqCoIijo

@ガベージコレクタ If I changed my user name to Jasper Loy, would you like me?

@skullpatrol: Yes. I will like both of you :-)

@skullpatrol I think your sentence in tenses is wrong.

i think "would" is implicitly futuristic

i am a linguist.

just kidding.

and another... math.stackexchange.com/questions/227396/…

@DanBrumleve Is that visual proof that I should change my name to "skeletor"?

And yes that moderator was ignoring me.

it is a proof of your confusion.

QED

we're all in this together yo

childhoodrelived.files.wordpress.com/2012/08/…

thanx

why have i been doing SE on even days?

math.stackexchange.com/users/1284/…

last two weeks in particular

Most of your reputation gains are even also.

short and sweet and slightly subtle math.stackexchange.com/a/227416/1284

if it is right :)

that's because recently it's my answers that have been upvoted and answer rep is 10 which is even.

ic

hi @JayeshBadwaik

but the bidiurnal property is a mystery to me

@skullpatrol Hi!!

answer #100 i think that's enough for today math.stackexchange.com/questions/227417/lim-x-to-fracx-x/…

in 3 minutes again! :)

hi @OldJohn

@skullpatrol Hi there

@OldJohn As a teacher, what is your opinion on the quotation of Galileo: " You cannot teach a man anything; you can only help him discover it in himself."

added homework: math.stackexchange.com/questions/227417/lim-x-to-fracx-x

is homework a proper inference in this case?

@skullpatrol He is probably right, I think

@OldJohn Discovering something in yourself, and internalizing something are different, right?

possibly - but don't forget that words like "internalizing" didn't exist in 16th century Italian language :)

yeah because that which is internalized necessarily comes from an external place.

whereas that which is found within is found there.

it wouldn't be internalized if it was already internal.

@OldJohn i'm not so sure wikiled.com/Latin-English-induo-default.aspx

induo

i bring within?

i lead within, rather.

i lead in.

@DanBrumleve Maybe, but I am not convinced

Maybe he's saying that you can only help someone teach themselves?

Thus discovering something they already knew.

surely galileo wasn't the first to think of it.

... if the latin word encapsulates the meaning.

To me "internalizing" is the same as memorizing...

same here... but what about its opposite?

forgetting ??

discovering.

In my opinion, before you get to discovering you must "understand."

nah it happens at the same time.

or rather it can't be proven that it happens at distinct times. :)

@DanBrumleve Did you understand before or after you discovered that?

before, actually i didn't mean to find one quite so mean but it was at least close to what i meant.

:)

QED

where do you draw the line between messing around and creating a new field? edge.org/3rd_culture/mandelbrot04/mandelbrot04_index.html

i like how mandelbrot talks about "creating a new field". it's such an egotistical concept but his humility shines through.

tldr

it's in the first few paragraphs

busted by Gerry again. math.stackexchange.com/questions/227415/… how to get that dude into chat?

@skullpatrol what is your academic background?

i downvoted you here math.stackexchange.com/questions/52974/… but now i'm suddenly unsure if my point is correct.

i forgot about how bbp works; if we keep the state that allowed us to compute the quadrillianth digit of pi, can't we get the digit at index 10^15+1 quite easily? that's what i'm assuming in my comment.

... in base 2 in any case.

although i thought i had read that bbp was adapted to other bases.

gnight